Understanding Particle Degree of Freedom: 3N dof for N Particles Explained

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SUMMARY

The discussion clarifies that a particle possesses 3 degrees of freedom (dof), leading to the conclusion that N particles have 3N dof. It emphasizes that these degrees of freedom pertain solely to translational motion, as classical mechanics considers particles to have zero spatial extent. Consequently, rotational motion does not contribute additional degrees of freedom, resulting in the assertion that particles do not possess rotational energy in this context.

PREREQUISITES
  • Understanding of classical mechanics principles
  • Familiarity with the concept of degrees of freedom in physics
  • Knowledge of translational versus rotational motion
  • Basic grasp of particle dynamics
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  • Research the implications of degrees of freedom in statistical mechanics
  • Explore the concept of rotational motion in rigid body dynamics
  • Learn about the differences between classical and quantum mechanics regarding particle behavior
  • Investigate the role of spatial extent in defining particle properties
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Students and professionals in physics, particularly those studying classical mechanics, particle dynamics, and the foundational concepts of motion and energy.

babbar.ankit
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A particle has 3 degree of freedom (dof) , so we write 3N dof for N particles...
But I have a fundamental doubt: 3 dof means we consider only transitional motion of particle?
... why can't we say 6 dof?
 
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Because, in classical mechanics, a particle is said to have zero spatial extent, and hence, insofar it rotates about an axis going through its C.M, the whole particle lies on the axis of rotation and thus do not have any rotational energy in addition to its translational energy.

Thus, in classical mechanics, rotation of infinitesemal particles is dynamically irrelevant.
 

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